Gov. Robert F. McDonnell on Monday said it was “way too early” after the Connecticut school massacre to know whether new gun control laws are warranted.

“Just a couple of days after a horrific, unfathomable tragedy with so many little 6-year-old kids getting gunned down by multiple gunshot wounds, I still can’t quite come to terms with it,” McDonnell (R) told reporters Monday. “My wife and I sat in front of that TV just sobbing Friday. Having five children ... I just cannot imagine the evil and horror that occurred in that classroom.

“So for me, it’s way too early to start reacting or overreacting with what the right policies might be. I think there’ll be a time to reflect maybe over the next 30 days,” he said, referring to the General Assembly session that begins Jan. 9.

McDonnell was asked about the shooting by reporters Monday morning, after he had presented budget amendments to the General Assembly’s money committees.

He issued an order Monday directing school divisions across the state as well as his secretaries of public safety and education to review school safety. Secretary of Education Laura Fornash and Secretary of Public Safety Marla Graff Decker were asked to review recently submitted school safety audits with local superintendents and to identify any changes in procedures or additional resources needed to ensure school safety.

Asked if he thought whether the time had come to post armed guards at every school, McDonnell said: “I hope not. I think that creates another psychological negative impact on the young people — first thing they see is an armed officer walking in the door.”

But McDonnell added: “What’s going to work? Because whatever’s going to work, I agree. There’s no price tag you can put on the precious lives that have been lost in this case.”

State Sen. Janet D. Howell (D-Fairfax) said she thought the mass shooting, which claimed the lives of 20 first-graders and 7 adults, cried out for gun-control measures.

“If this isn’t the right time, what is the right time?” she asked. “We have just lost 20 children, 6- and 7-year-olds. When would be the right time if it isn’t now?”

Howell said that in the aftermath of the Newtown shooting, she decided to submit legislation to close the “gun show loophole,” which allows people to buy guns at such events without background checks.

She acknowledged that such a law apparently would not have prevented Friday’s shooting, which authorities have said was carried out with a legally purchased military-style rifle. But she said the measure is one that might have a chance of passing in Virginia.

“I think there are many different approaches we have to take,” Howell said. “I think that’s the best shot for Virginia ... because so many guns are going without any background checks. ... I think while people are focused on it, we have to do everything we can. I’ve put it [the bill] in in the past. It didn’t go anywhere. But I think this year, I’m hopeful that people will come to their senses.”

Limiting gun rights would require an about-face by the General Assembly, which has been more inclined to loosen restrictions on firearms. Early this year, legislators repealed a 19-year-old law that had limited handgun purchases to one per month. They also stripped localities of the right to require fingerprints from people applying for concealed handgun permits.

But the horror of Friday’s shooting has prompted some strong gun-rights supporters to shift their positions. Sen. Mark Warner (D-Va.), who has an A rating from the National Rifle Association, said in Richmond Monday that he would push for “reasonable restrictions,” particularly on assault weapons.